Transition section for beam waveguides using aperture-limited lenses



OR 3v4109623 Nov. 12, 1968 H. w. KOGELNIK 3,410,623

TRANSITION SECTION FOR BEAM WAVEGUIDES USING APERTURE-LIMITED LENSESFiled March 9, 1965 5 Sheets-Sheet l //v VENTOR y H. W. KOGEL/V/K A TTORNEV Nov. 12, 1968 H. w. KOGELNIK 3,410,623

TRANSITION SECTION FOR BEAM WAVEGUIDES USING APERTURE-LIMITED LENSESFlleu March 9, 1965 5 Sheets-Sheet 2 mm a 2 1.. If n1! JILII! rI mm, WI.g mm 9 Q MN m Nov. 12, 1968 H. w. KOGELNIK 3,410,523

TRANSITIC'N SECTION FOR BEAM WAVEGUIDES USING APERTURE-LIMITEID LENSESI5 Sheets-$heet 3 Filed March 9. 1965 United States Patent 0 ABSTRACT OFTHE DISCLOSURE This application describes a transition section,comprising two aperture-limited lenses. for coupling optical wave energybetween two dissimilar beam waveguides which have similar mode patterns.By suitably spacing the lenses and selecting their focal lengths, themode pattern of one guide can be scaled to match the mode pattern of theother guide. Under these conditions, no mode conversion takes place atthe transition, and the iterative loss is the same for each lens in thestructure.

This invention relates to transition sections for couplingelectromagnetic wave energy of very short wavelengths between dissimilarbeam waveguides.

With the advent of the laser as a means for generating coherent waveenergy in the infrared, visible and ultraviolet portions of thefrequency spectrum, to be referred to hereinafter collectively asoptical waves, there has arisen concurrently a need for guiding meansfor the long distance transmission of such wave energy.

In an article entitled Experimental Studies on a Beam Waveguide forMillimeter Waves, published in the May 1961 issue of the Institute ofRadio Engineers Transactions on Antennas and Propagation, pp. 252-263,I. R. Christian and G. Goubau describe a so-called beam" waveguide forpropagating millimeter waves. A beam waveguide of this general type canalso be used at optical frequencies, as indicated by A. G. Fox and T. Liin their paper entitled Resonant Modes in a Maser Interferometer,published in the March 1961 issue of the Bell System Technical Journal.(Also see the paper entitled Confocal Multimode Resonators forMillimeter Through Optical Wavelength Masers, by G. D. Boyd and J. P.Gordon published in the same issue.)

In its simplest form a beam waveguide comprises a plurality of uniformlyspaced irises through which the wave energy propagates. The propagationcharacteristics of the waveguide are a function of the iris radii, theiristo-iris spacing and the wavelength of the wave energy.

More generally, however, the beam waveguide consists of a sequence ofaperture-limited lenses. The propagation characteristics of the lensbeam waveguide are also a function of the focal length of the lenses.

While the lens and the iris beam waveguides are referred to separatelyand are discussed separately in the detailed description containedhereinbelow, it should be noted that the iris waveguide can be regardedfor present purposes as a special lens waveguide in which the focallength of the lens is infinite.

As an optical waveguide is typically much larger in cross-sectionaldimensions than the wavelength of the wave energy propagating therein,it is capable of supporting many higher order modes. In an ideal systemin which the waveguide is perfectly uniform, the wave energy wouldpropagate undisturbed. However, it is recognized that in any practicaltransmission system it is generally necessary, for various reasons, tochange guide sizes. For example, straight sections of waveguide,extending over long distances are preferably made of large diameterwaveguide to minimize ditfraction losses. On

the other hand, curves are more efficiently negotiated by smallerdiameter waveguide. Thus, it is apparent that any practical transmissionsystem will afford ample opportunity to disturb the propagation of thewave energy unless appropriate means are provided to match the modepatterns of the two dissimilar waveguides. In the absence of suchmatching of the mode patterns, conversion of the Wave energy from thedesired modes to other spurious and undesired modes occurs with anaccompanying loss of power.

It is accordingly an object of the present invention to transfer waveenergy between two dissimilar beam waveguides with minimal modeconversion.

In accordance with the present invention, the parameters of thedissimilar waveguides are selected so that their mode patterns aresimilar. A transition section, comprising a series of lenses, isdesigned to couple these dissimilar waveguides by scaling the modepattern of each waveguide so as to match the mode pattern of the otherguide.

In a first embodiment of the invention, a two-lens transition sectionfor coupling a pair of dissimilar aperturelimited lens, beam waveguidesis described. In a second illustrative embodiment of the invention, atwo-lens transition section is used to couple dissimilar iris beamwaveguides. More generally, however, a transition section in accordancewith the invention can be used to couple any two dissimilar wavesupporting structures whose mode patterns are scaled versions of eachother.

For large aperture changes it may be advantageous to use additionallenses in the transition section. Accordingly, a three-lens illustrativeembodiment of the invention is also described.

These and other objects and advantages, the nature of the presentinvention, and its various features, will appear more fully uponconsideration of the various illustrative embodiments now to bedescribed in detail in connection with the accompanying drawings, inwhich:

FIG. 1 shows a transition section, in accordance with the presentinvention, for coupling two dissimilar aperture-limited lens beamwaveguides;

FIG. 2 shows a transition section used to couple two dissimilar irisbeam waveguides;

FIG. 3 shows, in perspective, an optical transmission path including twodissimilar beam waveguides coupled together by means of a two-lenstransition section;

FIG. 4 shows a two-lens transition section used to couple a cavityresonator to a beam waveguide;

FIG. 5 shows, for purposes of explanation, the use of two, two-lenstransition sections; and

FIG. 6 shows a three-lens transition section equivalent to the two,two-lens sections shown in FIG. 5.

Referring to FIG. 1, there is shown a beam wave transmission systemcomprising two dissimilar beam waveguides 10 and 11 coupled together bymeans of a transition section 12.

Beam waveguide 10 comprises a plurality of substantially identical,equally spaced aperture-limited lenses 13. Each of the lenses has afocal length f and an effective aperture radius a The lens-to-lensspacing is equal to 11,. Similarly, waveguide 11 comprises a pluralityof substantially identical, equally spaced aperture-limited lenses 14,each of which has a focal length f and an effective aperture radius aThe lens-to-lens spacing for waveguide 11 is d Coupling between the twodissimilar waveguides 10 and 11 is effected by means of the transitionsection 12. In accordance with the invention, one embodiment oftransition section 12 comprises two lenses, 15 and 16, of focal lengthsF and F respectively. Lens 15, adjacent to waveguide 10, has the sameaperture radius a as the lenses 13 in waveguide 10 have, and is locateda distance d equal to the lens-to-lens spacing in waveguide 10, from thelast, or terminal, lens in this guide.

Lens 16, adjacent to waveguide 11, has the same aperture radius a aslenses 14 have, and is spaced a distance d equal to the lens-to-lensspacing in waveguide 11, from the terminal lens in guide 11. Thedistance between the two transition lenses 15 and 16 is given as D.

The centers of the lenses are preferably located along a commonlongitudinal axis.

While the lenses 13 and 14, and the lenses in the transition section areillustrated as conventional glass lenses, it should be understood thatthe invention is not limited to any particular type of lens. That is,the lenses can be made of either glass or plastic material or,alternatively, they can be gas lenses of the type described by D. W.Berreman and S. E. Miller in their copending application Ser. No.379,175, filed June 30, 1964 and assigned to applicants assignee.

Wave energy applied to a beam waveguide of the type described above, isfocused by each of the lenses and a reiterative mode pattern isestablished. Wave energy which does not fall within the aperture of thelenses is not focused but is either intercepted and attenuated, orotherwise removed from the useful beam.

The transverse distribution of wave energy established in any beamwaveguide is a function of the parameters of the waveguide and, inparticular, can be characterized by a Fresnel N number for the waveguidegiven by and the parameter where a is the aperture radius,

d the lens-to-lens spacing,

j the focal length of the lenses, and

A the wavelength of the wave energy.

If two waveguides are dissimilar in that they have differentlens-to-lens spacings, different lens focal lengths and differentaperture radii but, nevertheless, have equal parameters N and G, themode patterns for the two waveguides are similar and scaled in the ratioof the aperture radii.

In accordance with the present invention, the transition section 12 isdesigned to connect two dissimilar waveguides. The spacing D of thetransition lenses 15 and 16, and their focal lengths F and F are sochosen that essentially no mode conversion takes place at the transitionand the iteration loss is the same for each aperture of the system.Aperture diffraction effects are taken into account as these areimportant in practical beam waveguides having Fresnel numbers of theorder of unity and smaller.

In order that no mode conversion takes place in the transition section,the separate waveguides and 11 are first designed to have similar modepatterns. In terms of the parameters of the waveguides, this means thatthe Fresnel numbers and the G parameters of the two waveguides are madeequal. That is,

When these conditions are fulfilled, the mode patterns of the twowaveguides are scaled versions of each other. It is known that the modepattern of a beam waveguide is reproduced at each lens aperture. Thus,if lens in the transition section 12 had a focal length f equal to thatof the lenses 13 in guide 10, the mode pattern of guide 10 would simplybe reproduced by lens 15 at a distance d from this lens. However, whatis sought is a scaled mode pattern. As shown by J. P. Gordon and H.Kogelnik, in their article Equivalence Relationships among SphericalMirror Optical Resonators, published in the November 1964 Bell SystemTechnical Journal, pp. 2873-2886, a scaled version of the mode patterncould be produced, but at a different location, by changing the focallength of lens 15 from f to some other value. In particular, to exactlymatch the mode pattern of the second Waveguide 11, the mode pattern ofWaveguide 10 must be scaled by a factor a /a From the scaling laws givenby Gordon et al., the scaled pattern would appear at a distance a2 a t zfrom lens 15.

It is, therefore, at this separation that the second transition sectionlens 16 is located. D, therefore, is the spacing between the transitionsection lenses 15 and 16.

The focal length of lens 15 to produce this scaling is given by l f1 1 2Similarly, to scale the wave pattern of guide 11 to that The beamwaveguides 10 and 11 in FIG. 1 include lenses of finite focal length ateach aperture position. In FIG. 2 there is illustrated a modified beamwaveguide in which aperture-limited lenses of infinite focal length(i.e., irises) are used. Thus, in FIG. 2 the first waveguide 20comprises a plurality of equally spaced, opaque annular members 22, eachof which has an aperture 23 of radius a Similarly, waveguide 21comprises a plurality of equally spaced, opaque annular members 24, eachof which has an aperture 25 of radius a Assuming, as before, that theiris-to-iris spacings d, and d and the aperture radii a and a are chosento produce similar mode patterns in the two waveguides, the designformulae for the transition section lenses 26 and 27 are also given byEquations 6, 7 and 8 except that f; and f the aperture focal lengths,are now equal to infinity. Making this substitution, Equations 6 and 7reduce to and (1 and In general, however, the pipes and the annularmembers support and protect the lenses, but play no substantial part indefining th transmission characteristics of the waveguides. Thesecharacteristics are basically defined by the properties and spacings ofthe lenses as explained hereinabove.

Transition section 32 comprises the two lenses 39 and 40 supported in aconical section of pipe 41 by means of the annular members 42 and 43.

As explained above, by omitting the lenses 33 and 34, waveguides 30 and31 can be converted from aperturelimited lens beam waveguides to irisbeam waveguides.

Recognizing that a cavity resonator, such as is used in a laser, is theequivalent of a series of equally spaced lenses, :1 transition sectionin accordance with the teachings of the present invention, can be usedto couple a cavity resonator to a beam waveguide. Such an arrangement isillustrated in FIG. 4, which shows a cavity resonator coupled to a beamwaveguide 51 by means of a transition section 52.

Cavity resonator 50 comprises a pair of mirrors 53 and 54 of radius rand aperture radius a spaced apart a distance d As the focal length f ofeach of the mirrors is equal to r 2, cavity 50 can be considered theequivalent of a beam waveguide comprising a plurality of lenses of focallength f aperture radius a and lens-to-lense spacing d The designprocedure for coupling cavity 50 to beam waveguide 51 is as givenhereinabove, with the exception that lens 55 in transition section 52 islocated immediately adjacent to one of the cavity mirrors 54 which ispartially transmissive. The other lens 56 in transition section 52,however, is spaced a distance d equal to the lens-to-lens spacing ofguide 51, from the terminal lens 57 of guide 51. The aperture radius oflens 55 is equal to a the aperture radius of cavity 50. The apertureradius of lens 56 is a equal to the aperture radius of the lenses inguide 51. The focal lengths of lenses 55 and 56 and their spacing D aregiven by Equations 5, 6 and 7. Advantageously, mirror 54 and lens 55 canbe combined into a single, unitary element.

Heretofore, a two-lens transition section has been considered. However,in order to accommodate large changes in guide diameters, the focallengths of the lenses necessary in a two-lens section become very short.In some instances it may, therefore, become more practical to use threeor more transition lenses of longer focal lengths, rather than twolenses having very short focal lengths.

The design formulae of a three or more lens transition section can bederived by considering the total transition to occur in stages. Forexample, in FIG. 5, a transition between beam waveguides 60 and 61 ismade in two stages by means of two transition sections 62 and 63connected by an intermediate section of waveguide 64. The guideparameters are indicated for each of the guides and as 1: l. f1)! (2! 2)f2) and (3! 3: f3): respectively.

For similar mode patterns, we have From Equations 5, 6 and 7 theparameters for each of the transition sections can be computed. Fortransition The focal lengths of lenses 1 and 2 in transition section 62are given by FY1051. 1 1 and 2 fs z 1 (18) respectively.

Similarly for transition section 63,

The focal lengths of lenses 2' and 3 of transition 63 are given by and 11 1 a .1 a fa s 2 respectively.

If now the length of the intermediate section of guide is reduced tozero, as illustrated in FIG. 6, lenses 2 and 2, which have the sameaperture radius a can be com bined and replaced by a single lens 22' offocal length F given by Equations 16, 17, 19 and 22 are, thus, thedesign formulae for the three-lens transition section 65, in accordancewith the present invention.

Since a the aperture radius of the center lens, can be arbitrarilyselected within the range a a a an advantageous selection can be made toproduce a linear taper transition section. This can be done by selectinga such that D D2 Solving Equation 23 for a in terms of a and a andcombining Equation 23 with Equations l6, 17, 19, 21 and 22 gives, forthe linear taper transition section,

It is apparent that by a similar process, the design formulae for atransition taper having four or more lenses can readily be obtained.

It is to be understood that the above-described arrangements areillustrative of a small number of the many possible specific embodimentswhich can represent appli cations of the principles of the inventionvNumerous and varied other arrangements can readily be devised inaccordance with these principles by those skilled in the art withoutdeparting from the spirit and scope of the invention.

What is claimed is:

1. An optical wave transmission system comprising two dissimilar lensbeam waveguides having similar mode patterns;

and means for coupling said waveguides comprising a pair of lenses ofaperture radii and focal lengths a F and a F respectively spaced apart adistance D, where 1 1 1 a2 --F;s a a wherein a and a are the respectiveaperture radii of the lenses in said two waveguides;

f and f are the respective focal lengths of the lenses in said twowaveguides; and

d and d are the effective lens-to-lens spacings for said two waveguides.

2. An optical wave transmission system comprising two dissimilar irisbeam waveguides having similar mode patterns;

and means for coupling said waveguides comprising a pair of lenses ofaperture radii and focal lengths a F and a F respectively spaced apart adistance D,

where ere i 2 (3-2- wherein a and a are the respective aperture radii ofthe irises in said two waveguides; and

a and d are the effective iris-to-iris spacings for said two waveguides.

a is aperture radius of said cavity;

a is the aperture radius of said waveguide;

d is the distance between cavity mirrors;

:1 is the aperture-to-aperture spacing of said waveguide; f is the focallength of said mirrors; and

f is the focal length of the waveguide apertures.

wherein 4. An optical wave transmission path including two dissimilarbeam waveguides;

the first of said guides comprising a plurality of equally spacedaperture-limited lenses each having a radius a,, focal length f andspaced apart a distance d the second of said guides comprising aplurality of equally spaced aperture-limited lenses each having a radius11 focal length f and spaced apart a distance d where the parameters Itand g for said guides are given by and means for coupling saidwaveguides comprising nrst, second and third lenses of radii and focallengths a F a F and a F respectively;

said lenses disposed between said waveguides in longitudinal successionwith the distance D between said first and second lenses given by a D1dl and the distance D between said second and third lenses given by (a sand the focal lengths of said lenses are JOHN K. CORBIN, PrimaryExmainer.

